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Extreme Numeral Systems

Short description

Design a small library that can store and display numbers in unusual numeral systems. Instead of sticking to the usual decimal (base-10), the program should handle systems like negative bases, matrix-based bases, or vector-based bases. The goal is not to prove mathematical theory, but to explore how alternative numeral systems can be represented and used in a clear, character-based output.

  • Numeral system / base – how numbers are expressed (e.g., binary, decimal, hexadecimal).
  • Negative base system – e.g., base -2, where powers alternate signs.
  • Non-standard bases – including fractional, complex, or vector-based systems.
  • Positional notation – numbers represented by digits and base powers.
  • Digit mapping – defining which symbols or values count as “digits.”

High-level technical guidelines

  • Use Python classes to represent a number together with its base and digits.
  • Store digit values in a list or array, where each position corresponds to a base power.
  • Implement simple display functions that print numbers clearly, showing both digits and base powers.
  • Start with easier cases (like base -2) before attempting matrix or vector bases.
  • Keep conversion optional: focus on representation, not necessarily on translating to decimal.

Using GPT with an expert persona

Using GPT with an expert persona can be a powerful way to simulate conversations with specialists, helping you quickly understand new concepts, explore different perspectives, and even discover useful features or requirements you might not have thought of on your own. Since this is a learning environment, you can also safely test the boundaries of what GPT knows and where it fails, without any risk to your job or reputation—making it a low-stakes, high-value tool for practicing how to ask good questions, evaluate answers critically, and deepen your understanding.

...but the responsibility for correctness and implementation is still yours!

When using the expert persona prompt, treat GPT as a helpful consultant, not an unquestionable authority. The answers can give you inspiration, explanations, or practical examples, but you should always double-check information in reliable sources and test ideas in your own code. Think of it as brainstorming with an expert partner—you get useful guidance, but the responsibility for correctness and implementation is still yours.

Sample expert persona prompt

You are a friendly but professional consultant helping early-year software engineering students design a library for unusual numeral systems. Take on the perspectives of a mathematician specializing in numeral systems, a theoretical computer scientist familiar with alternative representations, a software engineer implementing numeric libraries, a teacher skilled at simplifying abstract math for beginners, and a curious end-user who wants to see “weird numbers” displayed clearly. Be constructive, but let the students guide the discussion. If they drift from a professional tone, gently remind them. Always explain domain-specific terminology in simple words, and encourage students to ask questions if something is unclear. Ask as many clarification questions as needed to ensure you and the student are aligned before giving detailed answers.

Roles

  • Mathematician (numeral systems) – clarifies properties of negative, fractional, complex, and vector/matrix bases and their digit sets.
  • Theoretical computer scientist – advises on representations, positional notation generalizations, and edge-case behaviors.
  • Software engineer (numeric libraries) – designs clean classes/APIs for bases, digits, and operations with testable abstractions.
  • Teacher/explainer – translates abstract math into simple terms and intuitive examples for beginners.
  • Curious end-user (“weird numbers” fan) – validates that printed forms and annotations are readable and interesting.
  • Technical writer/UX for docs – ensures examples, digit maps, and base-power displays are consistent and easy to follow.